MATHEMATICS Compulsory Part PAPER 2 (Sample Paper)

HONG KONG EXAMINATIONS AND ASSESSMENT AUTHORITY HONG KONG DIPLOMA OF SECONDARY EDUCATION EXAMINATION

MATHEMATICS Compulsory Part PAPER 2 (Sample Paper)

Time allowed: 1 hour 15 minutes

1. Read carefully the instructions on the Answer Sheet. Stick a barcode label and insert the information required in the spaces provided.

2. When told to open this book, you should check that all the questions are there. Look for the words `END OF PAPER' after the last question.

3. All questions carry equal marks. 4. ANSWER ALL QUESTIONS. You are advised to use an HB pencil to mark all the answers on the Answer

Sheet, so that wrong marks can be completely erased with a clean rubber. 5. You should mark only ONE answer for each question. If you mark more than one answer, you will receive

NO MARKS for that question. 6. No marks will be deducted for wrong answers.

HKDSE-MATH-CP 2 ? 1 (Sample Paper)

Not to be taken away before the end of the examination session

66

There are 30 questions in Section A and 15 questions in Section B. The diagrams in this paper are not necessarily drawn to scale. Choose the best answer for each question.

Section A

1. (3a)2 a3 = A. 3a5 . B. 6a6 . C. 9a5 . D. 9a6 .

2. If 5 - 3m = 2n , then m = A. n . B. 2n - 5 . 3 C. -2n + 5 . 3 D. -2n +15 . 3

3. a2 - b2 + 2b - 1 = A. (a - b -1)(a + b -1) . B. (a - b -1)(a + b +1) . C. (a - b + 1)(a + b -1) . D. (a - b + 1)(a - b -1) .

HKDSE-MATH-CP 2 ? 2 (Sample Paper)

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4. Let p and q be constants. If x2 + p(x + 5) + q (x - 2)(x + 5) , then q = A. -25 . B. -10 . C. 3 . D. 5 .

5. Let f (x) = x3 + 2x2 - 7x + 3 . When f (x) is divided by x + 2 , the remainder is A. 3 . B. 5 . C. 17 . D. 33 .

6. Let a be a constant. Solve the equation (x - a)(x - a -1) = (x - a) . A. x = a + 1 B. x = a + 2 C. x = a or x = a + 1 D. x = a or x = a + 2

7. Find the range of values of k such that the quadratic equation x2 - 6x = 2 - k has no real roots. A. k < -7 B. k > -7 C. k < 11 D. k > 11

HKDSE-MATH-CP 2 ? 3 (Sample Paper)

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8. In the figure, the quadratic graph of y = f (x) intersects the straight line L at A(1, k) and B(7 , k) . Which of the following are true?

I. The solution of the inequality f (x) > k is x < 1 or x > 7 . II. The roots of the equation f (x) = k are 1 and 7 . III. The equation of the axis of symmetry of the quadratic graph of y = f (x) is x = 3 .

A. I and II only

y

B. I and III only

C. II and III only

y = f (x)

D. I , II and III

L

A

B

O

x

9.

The solution of 5 - 2x < 3 and 4x + 8 > 0 is

A. x > -2 .

B. x > -1 .

C. x > 1 .

D. -2 < x < 1 .

10. Mary sold two bags for $ 240 each. She gained 20% on one and lost 20% on the other. After the two transactions, Mary A. lost $ 20 . B. gained $ 10 . C. gained $ 60 . D. had no gain and no loss.

HKDSE-MATH-CP 2 ? 4 (Sample Paper)

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11. Let an be the nth term of a sequence. If a1 = 4 , a2 = 5 and an+2 = an + an+1 for any positive integer n , then a10 = A. 13 . B. 157 . C. 254 . D. 411 .

12. If the length and the width of a rectangle are increased by 20% and x% respectively so that its area is increased by 50% , then x = A. 20 . B. 25 . C. 30 . D. 35 .

13. If x , y and z are non-zero numbers such that 2x = 3y and x = 2z , then (x + z) : (x + y) = A. 3 : 5 . B. 6 : 7 . C. 9 : 7 . D. 9 :10 .

14. It is given that z varies directly as x and inversely as y . When x = 3 and y = 4 , z = 18 . When x = 2 and z = 8 , y =

A. 1 . B. 3 . C. 6 . D. 9 .

HKDSE-MATH-CP 2 ? 5 (Sample Paper)

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15. The lengths of the three sides of a triangle are measured as 15 cm , 24 cm and 25 cm respectively. If the three measurements are correct to the nearest cm , find the percentage error in calculating the perimeter of the triangle correct to the nearest 0.1% .

A. 0.8%

B. 2.3%

C. 4.7%

D. 6.3%

16. In the figure, O is the centre of the circle. C and D are points lying on the circle. OBC and BAD are straight lines. If OC = 20 cm and OA = AB = 10 cm , find the area of the shaded region BCD correct to the nearest cm2 . D

A. 214 cm2

B. 230 cm2 C. 246 cm2 D. 270 cm2

O A

B C

17. The figure shows a right circular cylinder, a hemisphere and a right circular cone with equal base radii. Their curved surface areas are a cm2 , b cm2 and c cm2 respectively.

r 2 r

Which of the following is true? A. a < b < c B. a < c < b C. c < a < b D. c < b < a

r r

2r r

HKDSE-MATH-CP 2 ? 6 (Sample Paper)

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18. In the figure, ABCD is a parallelogram. T is a point lying on AB such that DT is perpendicular to AB . It is given that CD = 9 cm and AT : TB = 1: 2 . If the area of the parallelogram ABCD is 36 cm2 , then the perimeter of the parallelogram ABCD is

A. 26 cm .

D

C

B. 28 cm .

C. 30 cm . D. 32 cm .

A T

B

19.

sin + cos(270? - ) =

cos 60? tan 45?

A. sin .

B. 3sin .

C. 2 sin - cos .

D. 2 sin + cos .

20. In the figure, AB = 1 cm , BC = CD = DE = 2 cm and EF = 3 cm . Find the distance between A and F correct to the nearest 0.1 cm .

A. 7.2 cm

A B

B. 7.4 cm C. 8.0 cm

C

D

D. 8.1 cm

E

F

21. In the figure, ABCD is a semi-circle. If BC = CD , then ADC =

A. 118? . B. 121? . C. 124? . D. 126? .

C

D

28?

A

B

HKDSE-MATH-CP 2 ? 7 (Sample Paper)

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22. In the figure, O is the centre of the circle ABCDE . If ABE = 30? and CDE = 105? , then AOC =

A. 120? . B. 135? . C. 150? . D. 165? .

D E

105?

O

C

A

30?

B

23. In the figure, ABCD is a parallelogram. F is a point lying on AD . BF produced and CD produced meet at E . If CD : DE = 2 :1 , then AF : BC =

E A. 1: 2 .

B. 2 : 3 . C. 3 : 4 .

F

A

D

D. 8 : 9 .

B

C

24. In the figure, ABC is a straight line. If BD = CD and AB = 10 cm , find BC correct to the nearest cm .

A. 8 cm D

B. 13 cm

C. 14 cm

D. 15 cm

40? C

B

20? A

HKDSE-MATH-CP 2 ? 8 (Sample Paper)

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